Identify which of the following functions is one-to-one.(1 point)

Question

Responses

g(x)=−6x4+2x−1
g left parenthesis x right parenthesis equals negative 6 x superscript 4 baseline plus 2 x minus 1

g(x)=x2−4x+1
g left parenthesis x right parenthesis equals x squared minus 4 x plus 1

g(x)=2x2
g left parenthesis x right parenthesis equals 2 x squared

g(x)=2x−4

Answer 1

To determine which of the given functions is one-to-one, a function is considered one-to-one if it passes the horizontal line test, meaning that each output value is produced by exactly one input value. This can also be checked by verifying that the function is either strictly increasing or strictly decreasing.

Let's analyze each function:

1. g(x) = -6x^4 + 2x - 1:

   • This is a polynomial function of degree 4, which typically means it can have multiple local maximums and minimums. Thus, it is likely not one-to-one.

2. g(x) = x^2 - 4x + 1:

   • This is a quadratic function (degree 2). Quadratic functions open either upwards or downwards and can have a vertex, meaning they can achieve the same value for different input values (e.g., both x = 1 and x = 3 yield the same output). Therefore, it is not one-to-one.

3. g(x) = 2x^2:

   • Similar to the previous function, this is also a quadratic function. Again, it opens upwards and can yield the same output for different input values (e.g., both x = 1 and x = -1 yield the same output), which means it is not one-to-one.

4. g(x) = 2x - 4:

   • This is a linear function, which has a constant slope and does not bend or curve. Linear functions are always one-to-one because each x-value corresponds to exactly one y-value.

Conclusion: The function that is one-to-one is g(x) = 2x - 4.